Advertisements
Advertisements
Question
A 10 kW drilling machine is used to drill a bore in a small aluminium block of mass 8.0 kg. How much is the rise in temperature of the block in 2.5 minutes, assuming 50% of power is used up in heating the machine itself or lost to the surroundings Specific heat of aluminium = 0.91 J g–1 K–1
Advertisements
Solution 1
Power of the drilling machine, P = 10 kW = 10 × 103 W
Mass of the aluminum block, m = 8.0 kg = 8 × 103 g
Time for which the machine is used, t = 2.5 min = 2.5 × 60 = 150 s
Specific heat of aluminium, c = 0.91 J g–1 K–1
Rise in the temperature of the block after drilling = δT
Total energy of the drilling machine = Pt
= 10 × 103 × 150
= 1.5 × 106 J
It is given that only 50% of the power is useful.
Useful energy, `triangle Q = 50/100 xx 1.5 xx 10^6 = 7.5xx10^5 J`
But `triangle Q = mctriangle T`
`:. triangle T = (triangle Q)/"mc"`
`= (7.5 xx 10^5)/(8xx10^3xx0.91)`
`= 103 ^@C`
Therefore, in 2.5 minutes of drilling, the rise in the temperature of the block is 103°C.
Solution 2
Power = 10 kW = 104 W
Mass, m=8.0 kg = 8 x 103 g
Rise in temperature, `triangle T =?`
`Time, t = 2.5 min = 2.5 xx 60 = 150 s`
Specific heat, `C = 0.91 Jg^(-1) K^(-1)`
Total energy = Power x Time = `10^4 xx 150 J`
`=15 xx 10^5 J`
As 50% of energy is lost
∴Thermal energy available
`triangle Q = 1/2 xx 15 xx 10^5 = 7.5 xx 10^5 J`
Since `triangle Q = mctrangle T`
`:.triangle T = triangleQ/mc = (7.5xx20^5)/(8xx10^3xx0.91) = 103^@C`
APPEARS IN
RELATED QUESTIONS
A hole is drilled in a copper sheet. The diameter of the hole is 4.24 cm at 27.0 °C. What is the change in the diameter of the hole when the sheet is heated to 227 °C? Coefficient of linear expansion of copper = 1.70 × 10–5 K–1.
The coefficient of volume expansion of glycerin is 49 × 10–5 K–1. What is the fractional change in its density for a 30 °C rise in temperature?
If an automobile engine is overheated, it is cooled by pouring water on it. It is advised that the water should be poured slowly with the engine running. Explain the reason.
A gas thermometer measures the temperature from the variation of pressure of a sample of gas. If the pressure measured at the melting point of lead is 2.20 times the pressure measured at the triple point of water, find the melting point of lead.
The density of water at 0°C is 0.998 g cm–3 and at 4°C is 1.000 g cm–1. Calculate the average coefficient of volume expansion of water in the temperature range of 0 to 4°C.
A steel rod is clamped at its two ends and rests on a fixed horizontal base. The rod is unstrained at 20°C.
Find the longitudinal strain developed in the rod if the temperature rises to 50°C. Coefficient of linear expansion of steel = 1.2 × 10–5 °C–1.
Solve the following problem.
In olden days, while laying the rails for trains, small gaps used to be left between the rail sections to allow for thermal expansion. Suppose the rails are laid at room temperature 27 °C. If maximum temperature in the region is 45 °C and the length of each rail section is 10 m, what should be the gap left given that α = 1.2 × 10–5K–1 for the material of the rail section?
A metal rod is heated to t°C. A metal rod has length, area of cross-section, Young's modulus and coefficient of linear expansion as 'L', 'A', 'Y' and 'a' respectively. When the rod is heated, the work performed is ______.
A uniform metallic rod rotates about its perpendicular bisector with constant angular speed. If it is heated uniformly to raise its temperature slightly ______.
Find out the increase in moment of inertia I of a uniform rod (coefficient of linear expansion α) about its perpendicular bisector when its temperature is slightly increased by ∆T.
At what temperature a gold ring of diameter 6.230 cm be heated so that it can be fitted on a wooden bangle of diameter 6.241 cm? Both diameters have been measured at room temperature (27°C). (Given: coefficient of linear thermal expansion of gold αL = 1.4 × 10-5 K-1).
Each side of a box made of metal sheet in cubic shape is 'a' at room temperature 'T', the coefficient of linear expansion of the metal sheet is 'α'. The metal sheet is heated uniformly, by a small temperature ΔT, so that its new temeprature is T + ΔT. Calculate the increase in the volume of the metal box.
If the length of a cylinder on heating increases by 2%, the area of its base will increase by ______.
Length of steel rod so that it is 5 cm longer than the copper rod at all temperatures should be ______ cm.
(α for copper = 1.7 × 10-5/°C and α for steel = 1.1 × 10-5/°C)
A solid metallic cube having a total surface area of 24 m2 is uniformly heated. If its temperature is increased by 10°C, calculate the increase in the volume of the cube.
(Given: α = 5.0 × 10−4°C−1)
A metal rod Y = 2 × 1012 dyne cm-2 of coefficient of linear expansion 1.6 × 10-5 per °C has its temperature raised by 20°C. The linear compressive stress to prevent the expansion of the rod is ______.
The increase in the dimensions of a body due to an increase in its temperature is called ______.
A metallic bar of Young’s modulus, 0.5 × 1011 N m−2 and coefficient of linear thermal expansion 10−5°C−1, length 1 m and area of cross-section 10−3 m2 is heated from 0°C to 100°C without expansion of bending. The compressive force developed in it is ______.
